Parallel and distributed Gröbner bases computation in JAS

This paper considers parallel Gröbner bases al-gorithms on distributed memory parallel comput-ers with multi-core compute nodes. We summa-rize three different Gröbner bases implementations: shared memory parallel, pure distributed memory parallel and distributed memory combined with shared memory parallelism. The last algorithm, called distributed hybrid, uses only one control communication channel between the master node and the worker nodes and keeps polynomials in shared memory on a node. The polynomials are transported asynchronous to the control-flow of the algorithm in a separate distributed data structure. The implementation is generic and works for all implemented (exact) fields. We present new perfor-mance measurements and discuss the performance of the algorithms.